Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:20 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a three-level growth model with
continuous factor indicators and one covariate on each of
the three levels
DATA: FILE = ex9.23.dat;
VARIABLE: NAMES = y1-y4 x w z level2 level3;
CLUSTER = level3 level2;
WITHIN = x;
BETWEEN = (level2) w (level3) z;
ANALYSIS: TYPE = THREELEVEL;
MODEL: %WITHIN%
iw sw | y1@0 y2@1 y3@2 y4@3;
iw sw ON x;
%BETWEEN level2%
ib2 sb2 | y1@0 y2@1 y3@2 y4@3;
ib2 sb2 ON w;
%BETWEEN level3%
ib3 sb3 | y1@0 y2@1 y3@2 y4@3;
ib3 sb3 ON z;
y1-y4@0;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a three-level growth model with
continuous factor indicators and one covariate on each of
the three levels
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 7500
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 6
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X W Z
Continuous latent variables
IW SW IB2 SB2 IB3 SB3
Variables with special functions
Cluster variables LEVEL3 LEVEL2
Within variables
X
Level 2 between variables
W
Level 3 between variables
Z
Estimator MLR
Information matrix OBSERVED
Maximum number of iterations 100
Convergence criterion 0.100D-05
Maximum number of EM iterations 500
Convergence criteria for the EM algorithm
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-03
Minimum variance 0.100D-03
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-02
Optimization algorithm EMA
Input data file(s)
ex9.23.dat
Input data format FREE
SUMMARY OF DATA
Number of LEVEL2 clusters 1500
Number of LEVEL3 clusters 50
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y1 0.491 -0.027 -8.550 0.01% -1.334 -0.048 0.500
7500.000 4.896 0.026 9.155 0.01% 1.045 2.359
Y2 0.824 -0.039 -9.778 0.01% -1.404 0.161 0.823
7500.000 7.219 0.047 10.352 0.01% 1.506 3.079
Y3 1.243 -0.001 -11.337 0.01% -1.616 0.357 1.221
7500.000 11.663 0.029 14.827 0.01% 2.124 4.129
Y4 1.627 0.048 -14.574 0.01% -1.951 0.561 1.585
7500.000 17.975 0.033 18.327 0.01% 2.648 5.185
X 0.008 0.008 -4.119 0.01% -0.842 -0.260 0.001
7500.000 1.013 0.013 4.022 0.01% 0.268 0.856
W 0.030 -0.083 -3.508 0.07% -0.792 -0.208 0.029
1500.000 1.007 0.037 2.958 0.07% 0.269 0.851
Z 0.017 -0.103 -2.337 2.00% -0.642 -0.245 -0.036
50.000 0.823 -0.067 2.055 2.00% 0.254 0.731
THE MODEL ESTIMATION TERMINATED NORMALLY
THE H1 MODEL ESTIMATION DID NOT CONVERGE. CHI-SQUARE TEST AND SAMPLE STATISTICS COULD NOT
BE COMPUTED.
MODEL FIT INFORMATION
Number of Free Parameters 25
Loglikelihood
H0 Value -56044.769
H0 Scaling Correction Factor 0.9835
for MLR
Information Criteria
Akaike (AIC) 112139.537
Bayesian (BIC) 112312.604
Sample-Size Adjusted BIC 112233.159
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
IW |
Y1 1.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 1.000 0.000 999.000 999.000
Y4 1.000 0.000 999.000 999.000
SW |
Y1 0.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 2.000 0.000 999.000 999.000
Y4 3.000 0.000 999.000 999.000
IW ON
X 0.986 0.018 55.928 0.000
SW ON
X 0.501 0.009 55.777 0.000
SW WITH
IW -0.011 0.012 -0.909 0.363
Residual Variances
Y1 0.981 0.037 26.763 0.000
Y2 1.011 0.026 38.621 0.000
Y3 1.007 0.023 44.625 0.000
Y4 0.959 0.038 24.949 0.000
IW 1.045 0.033 31.797 0.000
SW 0.212 0.010 21.462 0.000
Between LEVEL2 Level
IB2 |
Y1 1.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 1.000 0.000 999.000 999.000
Y4 1.000 0.000 999.000 999.000
SB2 |
Y1 0.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 2.000 0.000 999.000 999.000
Y4 3.000 0.000 999.000 999.000
IB2 ON
W 0.393 0.032 12.450 0.000
SB2 ON
W 0.193 0.015 12.595 0.000
SB2 WITH
IB2 0.006 0.020 0.314 0.754
Intercepts
Y1 0.000 0.000 999.000 999.000
Y2 0.000 0.000 999.000 999.000
Y3 0.000 0.000 999.000 999.000
Y4 0.000 0.000 999.000 999.000
IB2 0.000 0.000 999.000 999.000
SB2 0.000 0.000 999.000 999.000
Residual Variances
Y1 0.533 0.051 10.368 0.000
Y2 0.493 0.032 15.398 0.000
Y3 0.468 0.037 12.514 0.000
Y4 0.512 0.073 7.036 0.000
IB2 0.440 0.049 8.919 0.000
SB2 0.201 0.013 16.010 0.000
Between LEVEL3 Level
IB3 |
Y1 1.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 1.000 0.000 999.000 999.000
Y4 1.000 0.000 999.000 999.000
SB3 |
Y1 0.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 2.000 0.000 999.000 999.000
Y4 3.000 0.000 999.000 999.000
IB3 ON
Z 0.506 0.103 4.921 0.000
SB3 ON
Z 0.286 0.065 4.401 0.000
SB3 WITH
IB3 0.017 0.052 0.333 0.739
Intercepts
Y1 0.000 0.000 999.000 999.000
Y2 0.000 0.000 999.000 999.000
Y3 0.000 0.000 999.000 999.000
Y4 0.000 0.000 999.000 999.000
IB3 0.443 0.110 4.023 0.000
SB3 0.368 0.064 5.723 0.000
Residual Variances
Y1 0.000 0.000 999.000 999.000
Y2 0.000 0.000 999.000 999.000
Y3 0.000 0.000 999.000 999.000
Y4 0.000 0.000 999.000 999.000
IB3 0.568 0.110 5.142 0.000
SB3 0.195 0.037 5.321 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.576E-04
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IW SW X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
X 0 0 0
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
X 0 0 0 0 0
ALPHA
IW SW X
________ ________ ________
0 0 0
BETA
IW SW X
________ ________ ________
IW 0 0 5
SW 0 0 6
X 0 0 0
PSI
IW SW X
________ ________ ________
IW 7
SW 8 9
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IB2 SB2 W
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
W 0 0 0
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 10
Y2 0 11
Y3 0 0 12
Y4 0 0 0 13
W 0 0 0 0 0
ALPHA
IB2 SB2 W
________ ________ ________
0 0 0
BETA
IB2 SB2 W
________ ________ ________
IB2 0 0 14
SB2 0 0 15
W 0 0 0
PSI
IB2 SB2 W
________ ________ ________
IB2 16
SB2 17 18
W 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL3
NU
Y1 Y2 Y3 Y4 Z
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IB3 SB3 Z
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
Z 0 0 0
THETA
Y1 Y2 Y3 Y4 Z
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
Z 0 0 0 0 0
ALPHA
IB3 SB3 Z
________ ________ ________
19 20 0
BETA
IB3 SB3 Z
________ ________ ________
IB3 0 0 21
SB3 0 0 22
Z 0 0 0
PSI
IB3 SB3 Z
________ ________ ________
IB3 23
SB3 24 25
Z 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IW SW X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 2.448
Y2 0.000 3.610
Y3 0.000 0.000 5.831
Y4 0.000 0.000 0.000 8.987
X 0.000 0.000 0.000 0.000 0.000
ALPHA
IW SW X
________ ________ ________
0.000 0.000 0.000
BETA
IW SW X
________ ________ ________
IW 0.000 0.000 0.000
SW 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
IW SW X
________ ________ ________
IW 0.050
SW 0.000 0.050
X 0.000 0.000 0.507
STARTING VALUES FOR BETWEEN LEVEL2
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB2 SB2 W
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 2.448
Y2 0.000 3.610
Y3 0.000 0.000 5.831
Y4 0.000 0.000 0.000 8.987
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB2 SB2 W
________ ________ ________
0.000 0.000 0.000
BETA
IB2 SB2 W
________ ________ ________
IB2 0.000 0.000 0.000
SB2 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
IB2 SB2 W
________ ________ ________
IB2 0.050
SB2 0.000 0.050
W 0.000 0.000 0.504
STARTING VALUES FOR BETWEEN LEVEL3
NU
Y1 Y2 Y3 Y4 Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB3 SB3 Z
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
Z 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Z
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
ALPHA
IB3 SB3 Z
________ ________ ________
0.000 0.000 0.000
BETA
IB3 SB3 Z
________ ________ ________
IB3 0.000 0.000 0.000
SB3 0.000 0.000 0.000
Z 0.000 0.000 0.000
PSI
IB3 SB3 Z
________ ________ ________
IB3 0.050
SB3 0.000 0.050
Z 0.000 0.000 0.412
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.71621723D+05 0.0000000 0.0000000 EM
2 -0.57636758D+05 ************ 0.1952615 EM
3 -0.56176111D+05 1460.6471596 0.0253423 EM
4 -0.56059338D+05 116.7729583 0.0020787 EM
5 -0.56047719D+05 11.6187999 0.0002073 EM
6 -0.56045524D+05 2.1949573 0.0000392 EM
7 -0.56044975D+05 0.5496387 0.0000098 EM
8 -0.56044826D+05 0.1486447 0.0000027 EM
9 -0.56044785D+05 0.0413947 0.0000007 EM
10 -0.56044773D+05 0.0117124 0.0000002 EM
11 -0.56044769D+05 0.0033512 0.0000001 EM
12 -0.56044769D+05 0.0009641 0.0000000 EM
TECHNICAL 8 OUTPUT FOR THE H1 MODEL
TECHNICAL 8 OUTPUT FOR THE BASELINE MODEL
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.71655147D+05 0.0000000 0.0000000 EM
2 -0.71654179D+05 0.9680467 0.0000135 EM
3 -0.71653808D+05 0.3712120 0.0000052 EM
4 -0.71653657D+05 0.1505440 0.0000021 EM
5 -0.71653595D+05 0.0621802 0.0000009 EM
6 -0.71653569D+05 0.0259899 0.0000004 EM
7 -0.71653558D+05 0.0109517 0.0000002 EM
8 -0.71653554D+05 0.0046410 0.0000001 EM
9 -0.71653552D+05 0.0019745 0.0000000 EM
10 -0.71653551D+05 0.0008424 0.0000000 EM
Beginning Time: 23:20:57
Ending Time: 23:20:58
Elapsed Time: 00:00:01
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